pattern

System object: phased.IsotropicProjector
Namespace: phased

Plot isotropic projector directivity and patterns

Syntax

pattern(projector,FREQ)
pattern(projector,FREQ,AZ)
pattern(projector,FREQ,AZ,EL)
pattern(___,Name,Value)
[PAT,AZ_ANG,EL_ANG] = pattern(___)


Description

pattern(projector,FREQ) plots the 3D directivity pattern (in dBi) for the projector specified in projector. The operating frequency is specified in FREQ.

pattern(projector,FREQ,AZ) plots the projector directivity pattern at the specified azimuth angle.

pattern(projector,FREQ,AZ,EL) plots the projector directivity pattern at specified azimuth and elevation angles.

pattern(___,Name,Value) plots the projector pattern with additional options specified by one or more Name,Value pair arguments.

[PAT,AZ_ANG,EL_ANG] = pattern(___) returns the projector pattern in PAT. The AZ_ANG output contains the coordinate values corresponding to the rows of PAT. The EL_ANG output contains the coordinate values corresponding to the columns of PAT. If the 'CoordinateSystem' parameter is set to 'uv', then AZ_ANG contains the U coordinates of the pattern and EL_ANG contains the V coordinates of the pattern. Otherwise, they are in angular units in degrees. UV units are dimensionless.

Input Arguments

FREQ — Frequency for computing directivity and patterns

positive scalar | 1-by-L real-valued row vector

Frequencies for computing directivity and patterns, specified as a positive scalar or 1-by-L real-valued row vector. Frequency units are in hertz.

• For an antenna, microphone, or sonar hydrophone or projector element, FREQ must lie within the range of values specified by the FrequencyRange or FrequencyVector property of the element. Otherwise, the element produces no response and the directivity is returned as –Inf. Most elements use the FrequencyRange property except for phased.CustomAntennaElement and phased.CustomMicrophoneElement, which use the FrequencyVector property.

• For an array of elements, FREQ must lie within the frequency range of the elements that make up the array. Otherwise, the array produces no response and the directivity is returned as –Inf.

Example: [1e8 2e6]

Data Types: double

AZ — Azimuth angles

[-180:180] (default) | 1-by-N real-valued row vector

Azimuth angles for computing directivity and pattern, specified as a 1-by-N real-valued row vector where N is the number of azimuth angles. Angle units are in degrees. Azimuth angles must lie between –180° and 180°.

The azimuth angle is the angle between the x-axis and the projection of the direction vector onto the xy plane. When measured from the x-axis toward the y-axis, this angle is positive.

Example: [-45:2:45]

Data Types: double

EL — Elevation angles

[-90:90] (default) | 1-by-M real-valued row vector

Elevation angles for computing directivity and pattern, specified as a 1-by-M real-valued row vector where M is the number of desired elevation directions. Angle units are in degrees. The elevation angle must lie between –90° and 90°.

The elevation angle is the angle between the direction vector and xy-plane. The elevation angle is positive when measured towards the z-axis.

Example: [-75:1:70]

Data Types: double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

CoordinateSystem — Plotting coordinate system

"polar" (default) | "rectangular" | "uv"

Plotting coordinate system of the pattern, specified as the comma-separated pair consisting of CoordinateSystem and one of "polar", "rectangular", or "uv". When CoordinateSystem is set to "polar" or "rectangular", the AZ and EL arguments specify the pattern azimuth and elevation, respectively. AZ values must lie between –180° and 180°. EL values must lie between –90° and 90°. If CoordinateSystem is set to "uv", AZ and EL then specify U and V coordinates, respectively. AZ and EL must lie between -1 and 1.

Example: "uv"

Data Types: char

Type — Displayed pattern type

"directivity" (default) | "efield" | "power" | "powerdb"

Displayed pattern type, specified as the equal-sign-separated pair consisting of Type and one of

• "directivity" — directivity pattern measured in dBi.

• "efield" — field pattern of the sensor or array. For acoustic sensors, the displayed pattern is for the scalar sound field.

• "power" — power pattern of the sensor or array defined as the square of the field pattern.

• "powerdb" — power pattern converted to dB.

Example: "powerdb"

Data Types: char

Normalize — Display normalize pattern

true (default) | false

Display normalized pattern, specified as the comma-separated pair consisting of Normalize and a Boolean. Set this parameter to true to display a normalized pattern. This parameter does not apply when you set Type to "directivity". Directivity patterns are already normalized.

Data Types: logical

PlotStyle — Plotting style

"overlay" (default) | "waterfall"

Plotting style, specified as the equal-sign-separated pair consisting of Plotstyle and either "overlay" or "waterfall". This parameter applies when you specify multiple frequencies in FREQ in 2-D plots. You can draw 2-D plots by setting one of the arguments AZ or EL to a scalar.

Data Types: char

Polarization — Polarized field component

'combined' (default) | 'H' | 'V'

Polarized field component to display, specified as the comma-separated pair consisting of 'Polarization' and 'combined', 'H', or 'V'. This parameter applies only when the sensors are polarization-capable and when the 'Type' parameter is not set to 'directivity'. This table shows the meaning of the display options.

'Polarization'	Display
'combined'	Combined H and V polarization components
'H'	H polarization component
'V'	V polarization component

Example: 'V'

Data Types: char

Output Arguments

PAT — Element pattern

N-by-M real-valued matrix

Element pattern, returned as an N-by-M real-valued matrix. The pattern is a function of azimuth and elevation. The rows of PAT correspond to the azimuth angles in the vector specified by EL_ANG. The columns correspond to the elevation angles in the vector specified by AZ_ANG.

AZ_ANG — Azimuth angles

scalar | 1-by-N real-valued row vector

Azimuth angles for displaying directivity or response pattern, returned as a scalar or 1-by-N real-valued row vector corresponding to the dimension set in AZ. The columns of PAT correspond to the values in AZ_ANG. Units are in degrees.

EL_ANG — Elevation angles

scalar | 1-by-M real-valued row vector

Elevation angles for displaying directivity or response, returned as a scalar or 1-by-M real-valued row vector corresponding to the dimension set in EL. The rows of PAT correspond to the values in EL_ANG. Units are in degrees.

Examples

Response and Pattern of Isotropic Projector at Single Frequency

Examine the response and patterns of an isotropic projector operating between 1 kHz and 10 kHz.

Set the projector parameters and obtain the voltage response at five different elevation angles: -30°, -15°, 0°, 15° and 30°. All elevation angles at 0° azimuth angle. The voltage response is computed at 2 kHz.

projector = phased.IsotropicProjector('FrequencyRange',[1,10]*1e3);
fc = 2e3;
resp = projector(fc,[0,0,0,0,0;-30,-15,0,15,30]);

Draw a 3-D plot of the voltage response.

pattern(projector,fc,[-180:180],[-90:90],'CoordinateSystem','polar', ...
    'Type','power')

Response and Pattern of Isotropic Projector at Multiple Frequencies

Examine the response and patterns of an isotropic projector at three different frequencies. The projector operates between 1 kHz and 10 kHz. Specify the voltage response as a vector.

Set up the projector parameters, and obtain the voltage response at 45° azimuth and 30° elevation. Compute the responses at signal frequencies of 2, 5, and 7 kHz.

projector = phased.IsotropicProjector('FrequencyRange',[1 10]*1e3, ...
    'VoltageResponse',[90 95 100 95 90]);
fc = [2e3 5e3 7e3];
resp = projector(fc,[45;30]);
resp

resp = 1×3

    0.0426    0.0903    0.0708

Next, draw a 2-D plot of the voltage response as a function of azimuth.

pattern(projector,fc,[-180:180],0,'CoordinateSystem','rectangular', ...
    'Type','power')

More About

Directivity

Directivity describes the directionality of the radiation pattern of a sensor element or array of sensor elements.

Higher directivity is desired when you want to transmit more radiation in a specific direction. Directivity is the ratio of the transmitted radiant intensity in a specified direction to the radiant intensity transmitted by an isotropic radiator with the same total transmitted power

$$D=4\pi \frac{U_{\text{rad}}\left(\theta ,\phi \right)}{P_{\text{total}}}$$

where U_rad(θ,φ) is the radiant intensity of a transmitter in the direction (θ,φ) and P_total is the total power transmitted by an isotropic radiator. For a receiving element or array, directivity measures the sensitivity toward radiation arriving from a specific direction. The principle of reciprocity shows that the directivity of an element or array used for reception equals the directivity of the same element or array used for transmission. When converted to decibels, the directivity is denoted as dBi. For information on directivity, read the notes on Element Directivity and Array Directivity.

Version History

Introduced in R2017a